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The tangent to the hyperbola, x2 - 3y2 = 3 at the point (√3, 0) when associated with two asymptotes constitutes.
  • a)
    Isosceles triangle
  • b)
    An equilateral triangle
  • c)
    A triangle whose area is √3 sq.unit
  • d)
    A right isosceles triangle
Correct answer is option 'B,C'. Can you explain this answer?
Most Upvoted Answer
The tangent to the hyperbola, x2 - 3y2 = 3 at the point(√3, 0) w...
1, 2/√3) is given by the equation:

2x - 6y(dy/dx) = 0

To find dy/dx, we differentiate the equation of the hyperbola implicitly with respect to x:

2x - 6y(dy/dx) = 0

-6y(dy/dx) = -2x

dy/dx = x/3y

Substituting the coordinates of the given point, we get:

dy/dx = 1/(3√3)

Therefore, the equation of the tangent is:

2x - 6y(dy/dx) = 0

2x - 6(2/√3)(1/(3√3)) = 0

2x - 4/3 = 0

2x = 4/3

x = 2/3

Substituting x = 2/3 in the equation of the hyperbola, we get:

(2/3)2 - 3y2 = 3

4/9 - 3y2 = 3

-3y2 = 23/9

y = ±√(23/27)

Since the point (1, 2/√3) lies in the upper branch of the hyperbola, we take the positive value:

y = √(23/27)

Therefore, the equation of the tangent is:

2x - 4/3 = 0

or

x = 2/3
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The tangent to the hyperbola, x2 - 3y2 = 3 at the point(√3, 0) when associated with two asymptotes constitutes.a)Isosceles triangleb)An equilateral trianglec)Atriangle whose area is√3 sq.unitd)A right isosceles triangleCorrect answer is option 'B,C'. Can you explain this answer?
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